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101.
Dragan DJURCIC Aleksandar TORGASEV 《数学学报(英文版)》2006,22(3):689-692
In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc. 相似文献
102.
O. A. Brezhneva Yu. G. Evtushenko A. A. Tret’yakov 《Computational Mathematics and Mathematical Physics》2006,46(11):1896-1909
The theory of p-regularity is applied to optimization problems and to singular ordinary differential equations (ODE). The special variant of the method of the modified Lagrangian function proposed by Yu.G. Evtushenko for constrained optimization problems with inequality constraints is justified on the basis of the 2-factor transformation. An implicit function theorem is given for the singular case. This theorem is used to show the existence of solutions to a boundary value problem for a nonlinear differential equation in the resonance case. New numerical methods are proposed including the p-factor method for solving ODEs with a small parameter. 相似文献
103.
M. Hasanov 《Journal of Mathematical Analysis and Applications》2007,328(2):1487-1494
Nonlinear equations arising in the spectral theory of self-adjoint operator functions and related completeness problems for eigenvectors are studied. A separation theorem about the values of the Rayleigh functional on solutions of a nonlinear equation is proved. This theorem is used, as a new approach to establish completeness of eigenvectors for some classes of self-adjoint operator functions. Examples from matrix pencils are given. 相似文献
104.
Pavol Ševera 《Letters in Mathematical Physics》2006,75(3):273-277
We introduce an affine-invariant version of generating functions of symplectic transformations of affine symplectic spaces,
together with a generalization for other symmetric symplectic spaces. The composition of these functions has a nice connection
with the Moyal product. 相似文献
105.
Nicolas Bouleau 《Journal of Functional Analysis》2007,251(1):325-345
The error on a real quantity Y due to the graduation of the measuring instrument may be asymptotically represented, when the graduation is regular and fines down, by a Dirichlet form on R whose square field operator does not depend on the probability law of Y as soon as this law possesses a continuous density. This feature is related to the “arbitrary functions principle” (Poincaré, Hopf). We give extensions of this property to Rd and to the Wiener space for some approximations of the Brownian motion. This gives new approximations of the Ornstein-Uhlenbeck gradient. These results apply to the discretization of some stochastic differential equations encountered in mechanics. 相似文献
106.
P. A. V. Ferreira M. E. S. Machado 《Journal of Optimization Theory and Applications》1996,89(3):659-680
Projection and relaxation techniques are employed to decompose a multiobjective problem into a two-level structure. The basic manipulation consists in projecting the decision variables onto the space of the implicit tradeoffs, allowing the definition of a relaxed multiobjective master problem directly in the objective space. An additional subproblem tests the feasibility of the solution encountered by the relaxed problem. Some properties of the relaxed problem (linearity, small number of variables, etc.) render its solution efficient by a number of methods. Representatives of two different classes of multiobjective methods [the Geoffrion, Dyer, Feinberg (GDF) method and the fuzzy method of Baptistella and Ollero] are implemented and applied within this context to a water resources allocation problem. The results attest the computational viability of the overall procedure and its usefulness for the solution of multiobjective problems.This work was partially sponsored by grants from CNPq and FAPESP, Brazil. The authors are indebted to the anonymous reviewers for their valuable comments. 相似文献
107.
Y. Wardi 《Journal of Optimization Theory and Applications》1990,64(2):399-417
Stochastic algorithms for optimization problems, where function evaluations are done by Monte Carlo simulations, are presented. At each iteratex
i, they draw a predetermined numbern(i) of sample points from an underlying probability space; based on these sample points, they compute a feasible-descent direction, an Armijo stepsize, and the next iteratex
i+1. For an appropriate optimality function , corresponding to an optimality condition, it is shown that, ifn(i) , then (x
i) 0, whereJ is a set of integers whose upper density is zero. First, convergence is shown for a general algorithm prototype: then, a steepest-descent algorithm for unconstrained problems and a feasible-direction algorithm for problems with inequality constraints are developed. A numerical example is supplied. 相似文献
108.
Let (E, ¦·¦) be a uniformly convex Banach space with the modulus of uniform convexity of power type. Let be the convolution of the distribution of a random series inE with independent one-dimensional components and an arbitrary probability measure onE. Under some assumptions about the components and the smoothness of the norm we show that there exists a constant such that |{·<t}–{·+r<t}|r
q
, whereq depends on the properties of the norm. We specify it in the case ofL
spaces, >1. 相似文献
109.
Erik Aurell 《Journal of statistical physics》1990,58(5-6):967-995
I study poles and zeros of zeta functions in one-dimensional maps. Numerical and analytical arguments are given to show that the first pole of one such zeta function is given by the first zero ofanother zeta function: this describes convergence of the calculations of the first zero, which is generally the physically interesting quantity. Some remarks on how these results should generalize to zeta functions of dynamical systems with pruned symbolic dynamics and in higher dimensions follow. 相似文献
110.
V. I. Inozemtsev 《Journal of statistical physics》1990,59(5-6):1143-1155
Extra integrals of motion and the Lax representation are found for interacting spin systems with the HamiltonianH = (J/2)
j, k=1,j k
N
P(j – k)
j
k
, where one of the periods of the WeierstrassP function is equal toN. The Heisenberg and Haldane-Shastry chains appear as limiting cases of these systems at some values of the second period. The simplest eigenvectors and eigenvalues ofH corresponding to the scattering of two spin waves are presented explicitly for these finite-dimensional systems and for their infinite-dimensional version. 相似文献